1. My cat’s birthday is today
  2. It is possible to learn a subject and build anxiety in it due to prevalent stressful education environments
  3. Real, stress-free learning happens when you enjoy something…so learn to enjoy it first

Today is my cat’s 8th birthday! We got her when she just turned 6, so it has been 2 great years.

A flattering picture of my cat
A flattering picture of my cat

It is also a little over 2 years since I graduated from my engineering program and started my first full-time job as an applied scientist; and I noticed large changes in my mindset in how I view learning.

The biggest change was that there was a natural yearning to read and learn; especially when there is no pressure of GPA and taking 4-5 tough classes at once (usually higher-level math, an electrical/computer engineering course, a computer science course, and a general education course). Some people definitely have the right mindset in school where they take their time and enjoy the subjects they are taking without worrying much about what result or payoff will be. For me, and for most others I have met in my very intense engineering program, the primary driver of doing well in school was to do well after school. I feel now that this is just a recipe for hardship.

Learning experiences in math were espeically degraded due to this mindset. Unfortunately, being better at math wasn’t about seeing all the cool things that math could help you see. It was more the chain of:

Better test scores -> better gpa -> more coveted job -> better Facebook status at the end of 4 years -> ???

I won’t get into the toxic role of social media in all of this.

I also noticed that many of my peers and I had at least some amount of math anxiety due to the stressful environment in which math was taught in the engineering program. No doubt for many of the students coming from more intense high schools, the math education was stressful there as well; partly due to course structure and partly due to the competition between students (and parents). Anecdotally, similar anxiety about non-STEM courses was much lower…maybe because I felt less pressure to perform as well in those and maybe (probably) because I never took any of the higher level/intense/competitive versions of those courses.

Does anxiety in a subject necessarily mean that you are bad at the subject? Clearly no, or else I wouldn’t be in applied science and I imagine many engineers wouldn’t even be able to graduate. It seems to me anxiety about a subject doesn’t prevent you from using the learnings from that subject to get the job done; however, it does, sadly, prevent you from enjoying it and seeing all the amazing things about it.

Here is an interesting study about math anxiety in engineering freshmen.

Back to the present; now that I have this natural (organic?) desire to learn for the sake of learning it was time to set aside regrets about not learning in the best possible way in a place dedicated to learning and try to figure out how I can best learn some stuff I probably missed out on due to a bad mindset. How I can best learn some stuff and enjoy it.

This leads me to the second big change in how I viewed learning: if learning something is not time critical (and unless it has something to do with your livelihood, it almost never is) learn to enjoy the thing before trying to master it. Take a history topic, for example WW2, it might be tempting to scour a top 5 liberal arts school’s WW2 history course webpage, get the recommended reading, and start. If you already don’t know much about WW2, this will make you hate the topic because all you are doing is cramming in information without context (again). Who cares what some obscure politician was thinking at the time? Who cares about the economics of weapons production in the 1940’s? If you don’t have context, you definitely won’t care and you won’t be motivated to read a college level textbook on the topic.

Better first to find a lighter introduction that is written for an audience less informed on the subject. People might think they are above pop. sci and pop. history books, but they are an excellent starting point for someone just wanting to learn and enjoy a new topic without the stress.

I feel this same principle can be applied to STEM topics. In my case, when I took linear algebra in school, I did my homework, got good grades on the exams, and knew enough linear algebra to do machine learning. But what exactly is an eigenvector? It’s that thing you can use for SVD and to solve some differential equations right? Sure, but can you tell me what is cool about it?

Personally, for linear algebra, 3Blue1Brown’s excellent, short series on linear algebra opened my eyes to the coolness of the subject. I watched that series about a year after I started working, and I thought the way he explained linear algebra was so cool that I also wanted to be able to explain it like that.

axis of rotation gif
Three different rotations applied with 3 different eigenvectors

Most average people don’t care about what an eigenvector is. Most above-average people don’t care about what an eigenvector is. But by trying to re-learn linear algebra and making it cool in my own head, I found that I can make almost anyone think an eigenvector is cool without using any “math”…even if for just one moment. I take something I have in my hand, rotate it, and show them how all but one vector is changing when I apply a ‘rotation matrix’. It is trivial, and it is just the tip of the iceberg, but it is very satisfying to see someone with no background get why you think that thing is cool. And it is usually more than enough motivation to keep leanring more, and keep going deeper.

I feel that most education systems don’t take the time to answer that question, and it unfortunately falls on the students to take initiative to figure out why something is cool. And I wouldn’t count on a student doing that when they already have a ton of other work they need to finish before their next exam.

Maybe next time you try to learn a topic (math or otherwise) you’ll first try to answer the question: what is cool about this topic? It doesn’t have to apply to real life either; it can be totally abstract. As long as you think it is cool, that is all the motivation that is needed.

Like Feynman said, you don’t understand something until you can explain it simply. He also said “Hell, if I could explain it to the average person, it wouldn’t have been worth the Nobel prize”; but I think that for the vast majority of things we can learn, we should be able to tell the average person at least why it is cool.


  1. Math Anxiety In Engineering Freshman paper:
  2. 3Blue1Brown’s youtube channel:
  3. Sphere rotation gif: